Momentum conservation and self-forces reduction are challenges for all Particle-In-Cell (PIC) codes using spatial discretization schemes which do not fulfill the requirement of translational invariance of the grid Green’s function. We comment here on the topic applied to the recently developed Multi-Level Multi-Domain (MLMD) method. The MLMD is a semi- implicit method for PIC plasma simulations. The multi-scale nature of plasma processes is addressed by using grids with different spatial resolutions in different parts of the domain.